Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects
Numerical Analysis
2016-12-30 v1
Abstract
We consider an identification problem, where the state is governed by a fractional elliptic equation and the unknown variable corresponds to the order of the underlying operator. We study the existence of an optimal pair and provide sufficient conditions for its local uniqueness. We develop semi-discrete and fully discrete algorithms to approximate the solutions to our identification problem and provide a convergence analysis. We present numerical illustrations that confirm and extend our theory.
Cite
@article{arxiv.1612.08982,
title = {Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects},
author = {Harbir Antil and Enrique Otarola and Abner J. Salgado},
journal= {arXiv preprint arXiv:1612.08982},
year = {2016}
}